Long as you have some type of data whether its a monthly plan or a prepaid plan and have data you can turn data off on phone and still recieve text messages. But if no data connected to phone you wont recieve nothing

It depends a lot in what kind of text messages, if you mean SMS then yes you'll still receive them because they depend on your cell service, the only way you won't receive them is if you have your mobile phone on airplane mode. However, you won't 't receive Whatsapp texts nor Snapchats... because these depend on your mobile data.